Question: Daniel is 27 years older than Ashley. Eighteen years ago, Daniel was 4 times as old as Ashley. How old is Ashley now?
Answer: We can use the given information to write down two equations that describe the ages of Daniel and Ashley. Let Daniel's current age be $d$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $d = a + 27$ Eighteen years ago, Daniel was $d - 18$ years old, and Ashley was $a - 18$ years old. The information in the second sentence can be expressed in the following equation: $d - 18 = 4(a - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $d$ and substitute it into our second equation. Our first equation is: $d = a + 27$ . Substituting this into our second equation, we get the equation: $(a + 27)$ $-$ $18 = 4(a - 18)$ which combines the information about $a$ from both of our original equations. Simplifying both sides of this equation, we get: $a + 9 = 4 a - 72$ Solving for $a$ , we get: $3 a = 81$ $a = 27$.